Noncommutative localizations of a contractive quantum plane

Abstract

In the present paper we investigate the localizations in the sense of J. L. Taylor of the Arens-Michael-Fréchet algebras associated with noncommutative analytic spaces of a contractive q-plane representing its formal geometry. It turns out that all noncommutative Fréchet algebras obtained by the Fréchet algebra structure sheaves over open subsets from the topology bases are indeed localizations. That topological homology property of the structure sheaves results in the key properties of Taylor and Putinar spectra of the left Banach q-modules over the algebras of global sections.